In recent years high quality colour printers has became a norm. Two significant and related factors led to such being the norm, namely improvements in accuracy in colour reproduction and improvements in resolution. For ink jet printers, typical resolutions are 1200 dpi or higher, which translates into a printer ink dot size (and separation) of 20 microns or less. In many systems the ink jet printer may overprint regions multiple times to help minimise the effect of printer defects, such as blocked printer head nozzles. The optical density of a printed colour can be very sensitive to the precise value of the displacement between overprinted regions. This means that (for high quality at least) it is necessary to control or calibrate the exact displacement of the printer head between overprints.
Many approaches have been proposed for calibrating the movements of the printer head relative to the medium being printed on in a precise manner. The main approaches can be summaries as follows:                Measure (using the human eye, or more recently an optical sensor) optical density of an overlapping, interlaced dot pattern (also known as complementary dot patterns);        Measure alignment of a series of lines (visually inspection using the Vernier effect);        Measure alignment of an interlaced series of lines (Vernier effect using optical sensor); and        Measure (using a scanner) individual positions of sparse, but regular arrays of dots.        
Until recently the visually based methods have dominated so completely that visual inspection is assumed and is not usually mentioned explicitly. The more recent automatic methods are typically just simple modifications of the visual methods to allow simple optical sensors to monitor spatial variations in optical density. Measurement of individual dot positions, although fundamental, is quite unreliable due to the large variations in dot shape, position and size. There is also the difficulty of unambiguously locating isolated dots in large regions on the medium being printed upon.
With these weaknesses in the prior art methods in mind it is beneficial to consider more general and robust approaches to measurement.